Draw the graph for each of the equations x + y = 6 and x – y = 2 on the same graph paper and find the coordinates of the point where the two straight lines intersect.
Given equation, x + y = 6
⇒ y = 6 – x
When x = 0, then y = 6 – x
⇒ y = 6 – 0
⇒ y = 6
When x = 2, then y = 6 – x
⇒ y = 6 – 2
⇒ y = 4
When x = 4, then y = 6 – x
⇒ y = 6 – 4
⇒ y = 2
When x = 6, then y = 6 – x
⇒ y = 6 – 6
⇒ y = 0
Thus we have the following table,
X | 0 | 2 | 4 | 6 |
Y | 6 | 4 | 2 | 0 |
Given equation, x – y = 2
⇒ y = x – 2
When x = 0, then y = x – 2
⇒ y = 0 – 2
⇒ y = – 2
When x = 2, then y = x – 2
⇒ y = 2 – 2
⇒ y = 0
When x = 4, then y = x – 2
⇒ y = 4 – 2
⇒ y = 2
When x = 6, then y = 6 – 2
⇒ y = 6 – 2
⇒ y = 4
Thus we have the following table,
X | 0 | 2 | 4 | 6 |
Y | – 2 | 0 | 2 | 4 |
From the graph, it is clear that x + y = 6 and x – y = 2 intersects at (4, 2)
